For a function \(f: \mathcal {F}\rightarrow \Sigma ^*\)  with \(f(F^*)=\epsilon \) , Schrijver [1]} showed that
a smallest pre-feasible function \(\bar{f}\)  larger than \(f\)  can be well-defined. That is, any finite pre-feasible function \(f^*\)  larger than \(f\)  is also larger than \(\bar{f}\) .
Furthermore, Section 2.4 of  [1]} describes an algorithm for finding a smallest pre-feasible function \(\bar{f}\)  for a given function \(f\)  with \(f(F^*)=\epsilon \) .
It will be used as a subroutine for computing a \(T\) -linkage homotopic to \(\mathcal {W}\) .
The subroutine is based on the following lemma.
